A347638 Number of minimal dominating sets in the n-dipyramidal graph (for n > 3).

3, 7, 10, 15, 16, 18, 29, 31, 40, 48, 67, 82, 105, 143, 189, 255, 341, 474, 647, 892, 1236, 1719, 2393, 3330, 4656, 6503, 9094, 12719, 17807, 24931, 34907, 48895, 68490, 95951, 134420, 188338, 263885, 369743, 518080, 725940, 1017211, 1425346, 1997265, 2798671

Offset: 1

Author

Eric W. Weisstein, Sep 09 2021

Keywords

• nonn
• easy

Comments

The 3-dipyramidal graph deviates from this sequence because it has 4 minimal dominating sets while a(3) = 10.

Links

• Eric Weisstein's World of Mathematics, Dipyramidal Graph
• Eric Weisstein's World of Mathematics, Minimal Dominating Set
• Index entries for linear recurrences with constant coefficients, signature (2,0,-1,0,-1,0,2,-1).

Crossrefs

Cf. A253413.

Programs

Mathematica

Table[2 n + 1 + RootSum[1 - #^2 - #^3 - #^4 + #^6 &, #^n &], {n, 20}]
LinearRecurrence[{2, 0, -1, 0, -1, 0, 2, -1}, {3, 7, 10, 15, 16, 18, 29, 31}, 20]
CoefficientList[Series[(3 + x - 4 x^2 - 2 x^3 - 7 x^4 - x^5 + 15 x^6 - 7 x^7)/((-1 + x)^2 (1 - x^2 - x^3 - x^4 + x^6)), {x, 0, 20}], x]

Formula

a(n) = A253413(n)+2*n+1.

a(n) = 2*a(n-1)-a(n-3)-a(n-5)+2*a(n-7)-a(n-8).

G.f.: x*(3+x-4*x^2-2*x^3-7*x^4-x^5+15*x^6-7*x^7)/((-1+x)^2*(1-x^2-x^3-x^4+x^6)).